Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigDecimal;
import java.util.Arrays;
import java.util.StringTokenizer;

import static java.lang.Integer.parseInt;

/**
 * Maximization of Relational Expression
 */
public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line;
		String[] words;

		int N = parseInt(br.readLine());
		int[] a = new int[N];

		StringTokenizer st = new StringTokenizer(br.readLine());
		for (int i = 0; i < N; i++) a[i] = parseInt(st.nextToken());
		Arrays.sort(a);

		double max = 0.0;
		BigDecimal AB, CD;

		for (int i = 0; i < N - 3; i++) {
			AB = BigDecimal.valueOf(a[N - 1] + a[N - 2]);
			CD = BigDecimal.valueOf(a[i + 1] - a[i]);
			max = Math.max(max, AB.divide(CD, 7, BigDecimal.ROUND_HALF_UP).doubleValue());
		}

		AB = BigDecimal.valueOf(a[N - 1] + a[N - 4]);
		CD = BigDecimal.valueOf(a[N - 2] - a[N - 3]);
		max = Math.max(max, AB.divide(CD, 7, BigDecimal.ROUND_HALF_UP).doubleValue());


		AB = BigDecimal.valueOf(a[N - 3] + a[N - 4]);
		CD = BigDecimal.valueOf(a[N - 1] - a[N - 2]);
		max = Math.max(max, AB.divide(CD, 7, BigDecimal.ROUND_HALF_UP).doubleValue());

		System.out.format("%.6f%n", max);
	}
}